It is basically an iOS device with a remote controller and optional game controller. Graphics, audio, media, content pipeline should all work as normal. The only part of MonoGame that would need updating is handling the input. To support that, someone would need to get an Apple TV device and add the support for the remote and game controller. The game controller is optional for games, but support for the remote is required. The remote has a touch surface at the top that can be used to simulate a d-pad.
Apple TV also has no local storage for apps. All save games must use iCloud, so MonoGame's StorageDevice support will not be usable.
App packages are limited to 200MB. Extra data must be streamed from the App Store servers.